On the extraconnectivity of<i>k</i>-ary<i>n</i>-cube networks

Gu, Mei-Mei; Hao, Rong‐Xia; Li, Jianbing

doi:10.1080/00207160.2015.1091070

Cited by 19 publications

(7 citation statements)

References 16 publications

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“…n is an n-dimensional hypercube. There are various works concerning various topological and structural properties of this class of graphs in the literature, and some of the recent papers include [7,8,10,11,18,21].…”

Section: Some Results Which Follow From Theorem 32mentioning

confidence: 99%

On The automorphism groups of $us$-Cayley graphs

Mirafzal¹

2019

Preprint

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Let G be a finite abelian group written additively with identity 0, and Ω be an inverse closed generating subset of G such that 0 / ∈ Ω. We say that Ω has the property "us" (unique summation), whenever for every 0 = g ∈ G if there are s 1 , s 2 , s 3 , s 4 ∈ Ω such that s 1 + s 2 = g = s 3 + s 4 , then we have {s 1 , s 2 } = {s 3 , s 4 }. We say that a Cayley graph Γ = Cay(G; Ω) is a us-Cayley graph, whenever Γ is an abelian Cayley graph and the generating subset Ω has the property "us". In this paper, we show that if Γ = Cay(G; Ω) is a us-Cayley graph, then Aut(Γ) = L(G) A, where and A is the group of all automorphisms θ of the group G such that θ(Ω) = Ω. Then, we explicitly determine the automorphism groups of some classes of graphs, including Möbius ladders and k-array n-cubes.

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Section: Some Results Which Follow From Theorem 32mentioning

confidence: 99%

On The automorphism groups of $us$-Cayley graphs

Mirafzal¹

2019

Preprint

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“…This measure is the minimum number of nodes whose deletion disconnects the network G, and every remaining component has no less than s + 1 nodes. s-EC has been studied for many interconnection networks including k-ary n-cubes [5], augmented k-ary n-cubes [15], folded crossed cubes [8], generalized exchanged hypercubes [11], and alternating group graphs [18], and data center networks such as DCell [10] and BCube [17].…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of complete cubic networks based on extra conditional fault

Lv,

Liu,

Dong

et al. 2024

Preprint

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The reliability of multiprocessor systems is now a crucial concern in parallel computing. In fact, thanks to rapid and consistent technological advances in networking hardware and software, multiprocessor (core) systems have been successfully implemented. Consequently, there is a notable importance in examining the structures of interprocess communication, with a particular focus on investigating the fault tolerance and fault diagnosability of these structures to build a functionally efficient system. This paper investigates the $s$-extra connectivity ($s$-EC) and $s$-extra diagnosability ($s$-ED) of the complete cubic network $CCN(n)$. Specifically, we initially demonstrate that the $s$-EC of $CCN(n)$ is $\kappa_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}$ for $n\geq 3$ and $0\leq s\leq n-2$. Subsequently, we demonstrate that the $s$-ED under the PMC model is $t_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}+s$ for $n\geq 3$ and $1\leq s\leq n-2$. Similarly, under the MM* model, the $s$-ED is $t_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}+s$ for $n\geq 6$ and $1\leq s\leq \frac{n-2}{4}$. Finally, we conduct simulation experiments, and the results indicate that the $s$-EC consistently surpasses other known connectivities, including classical connectivity and $s$-component connectivity. Additionally, the $s$-ED consistently outperforms classical diagnosability and $s$-component diagnosability of $CCN(n)$.

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“…Obviously, κ (0) (G) � κ(G) for each linked incomplete graph G. erefore, the traditional connectivity may be regarded as a simplification of g-extra connectivity, and it is able to serve for more precisely measuring the consistency and error lenience for INs. e g-extra connectivity of numerous INs was widely investigated (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

The 2-Extra Connectivity of Wheel Networks

Feng

Wang

2020

Mathematical Problems in Engineering

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Connectivity is a significant metric for evaluating the error lenience of an interconnected net G=V,E. In the paper (Fàbrega and Fiol, 1996), the authors addressed the g-extra connectivity which is applied to better measure the consistency and error tolerance of G. As a special Cayley graph, the n-dimensional wheel network CWn has some desirable features. This paper shows that the g-extra connectivity of CWnn≥6 is 6n−12 when g=2.

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On the extraconnectivity ofk-aryn-cube networks

Cited by 19 publications

References 16 publications

On The automorphism groups of $us$-Cayley graphs

On The automorphism groups of $us$-Cayley graphs

Reliability analysis of complete cubic networks based on extra conditional fault

The 2-Extra Connectivity of Wheel Networks

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